一位國小教師實施數學探究教學之歷程與任務

The Process and Tasks of Inquiry-based Mathematics Instruction Implementation by an Elementary Teacher

本研究旨在探討數學探究教學的歷程及歷程中教師關注的教學任務。以一位主修數學教育的國小資深教師為對象，採個案研究法，透過教學錄影和訪談進行資料蒐集。結果發現個案教師的數學探究教學從呈現挑戰題開始，歷經連結理解、探究解題、精緻／一般化等階段，不同階段關注的教學任務不同：連結理解階段個案教師關注「提供線索」，協助學生理解題意與問題之所求；探究解題階段關注「要求說明」，藉此來發展學生的解題推理；精緻／一般化階段關注「順序化」學生的解題歷程，以得出後續應用的解題方法。個案教師的數學探究教學緊扣著數學解題的歷程，過程中透過提問和學生互動，意圖達成理解題意、發展解題、推理應用的教學目的。

The research purposes were to investigate the processes of inquiry-based mathematics instruction, and the tasks teachers concerned in the process. An experienced elementary teacher who majored in mathematics education participated in this study. This study adopted case study as the research method and collected data through recording video in the classroom and interviews with the teacher. The results indicated that the teacher posed a non-routine mathematical problem for students in the beginning of her instruction, then she went through the stages of linking understandings, problem solving through inquiry, and elaboration for generalization. At different stages, the teacher concerned different tasks: at the stage of linking understandings, the teacher focused on “providing hints” to help students to understand the problem and what is asked; at the stage of problem solving through inquiry, “asking for explanation” was her major concern in order to help students to develop mathematical reasoning for solving problem; “sequencing students’ thinking processes” was the focus at the stage of elaboration for further application. The processes of inquiry-based mathematics instructed by the teacher following the procedures of math problem solving. Teaching skills such as asking questions and interacting with students were often adopted by the teacher to achieve the instructional goals that included understanding the meaning of problems, development of problem-solving methods, and applying the methods to other problems with similar mathematical structure.